Mastering the Product Rule for Derivatives

This video tutorial covers the product rule for derivatives, explaining its formula and application. It provides three examples, demonstrating how to calculate derivatives of functions using the product rule, including complex and exponential functions. The tutorial emphasizes the importance of correctly applying the rule and offers tips for simplifying the process.

What is the first step in applying the product rule for derivatives?

• Subtract the derivative of the first function from the second function.

• Add the derivatives of both functions.

• Multiply the first function by the second function.

• Multiply the first function by the derivative of the second function.

When should you use the product rule?

• When two functions are being subtracted.

• When two functions are being multiplied.

• When two functions are being added.

• When two functions are being divided.

What is a good practice before applying the product rule?

• Ignore the derivatives.

• Find the derivatives of both functions separately.

• Simplify the functions first.

• Combine the functions into one.

In the first example, what is the derivative of the function 2x^2?

• 6x

• 2x

• 4x

• x^2

What is the simplified form of the derivative in the first example?

• 12x^3 + 2x

• 6x^3 + 2x

• 12x^2 + 2x

• 6x^2 + 2x

In the second example, what is the derivative of x^(1/2)?

• 2 / (√x)

• 2√x

• 1 / (√x)

• 1 / (2√x)

What is the derivative of x^3 + 2x^2 in the second example?

• 3x^2 + 4x

• 3x^3 + 4x^2

• 6x^2 + 4x

• 3x^2 + 2x

In the third example, what is the derivative of e^x?

• e^x

• x

• xe^x

• e^{x-1}

What is the simplified form of the derivative in the third example?

• 4e^x / x + x * 2e^x

• 2e^x / x + x * 4e^x

• 4e^x / √x + √x * 2e^x

• 2e^x / √x + √x * 4e^x

What should you be careful about when using the product rule?

• The order of addition.

• The order of multiplication.

• The order of subtraction.

• The order of division.